The baby, the first for the couple, is due in mid-October.
Kody, 43, and Robyn, 31, wed last year during the first season of Sister Wives. Kody is also married to Meri, Janelle and Christine. He has 16 other children, and Robyn has three from a previous marriage.
"I'm overjoyed," Kody told the magazine. "This connects Robyn and I together in a way that nobody can take away."
Sister Wives — which shows the inner workings of their plural family despite the fact that polygamy is outlawed — airs Sundays at 9/8c on TLC.